How do I delete an object?
You have to delete from object from Object Mode, not Edit Mode. You can switch between Object Mode and Edit Mode using the Tab key on your keyboard. You can also switch using he drop down menu on the bottom panel of the 3d View window.Then hit delete again (Function delete on Mac) and you will be able to Delete the object entirely, it will also disappear from the outliner. If you want to delete parts of your mesh use Edit Mode, if you want to delete the entire mesh use Object Mode.

Switch to Object Mode



Now you can delete